The generator matrix

 1  0  1  1  1  1  1  0
 0  1  1  2  0 2X+1  2  1
 0  0 2X  0  X 2X  X  0
 0  0  0  X  X 2X 2X  X

generates a code of length 8 over Z3[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+92x^12+320x^15+296x^18+16x^21+4x^24

The gray image is a linear code over GF(3) with n=24, k=6 and d=12.
This code was found by Heurico 1.16 in 0.000788 seconds.